The numerical implementation of the nonlinear Fourier transformation (NFT) for the nonlinear Shrodinger equation (NLSE) requires effective numerical algorithms for each stage of the method. The very first step in this scheme is the solution of the direct scattering problem for the Zakharov-Shabat system. One of the most efficient methods for the solution of this problem is the second-order Boffetta-Osborne algorithm . A review of numerical methods for direct NFT associated with the focusing NLSE is presented in . Among the methods considered in this paper only the Runge-Kutta method is of fourth order of approximation. However, the application of the Runge-Kutta method is limited by the potentials specified analytically. The NFT algorithms of higher order presented recently in  require special nonuniform distribution of the signal.
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